(a) Consider a futures contract and a forward contract written on the same underlying asset, with the same delivery date. Explain why the futures price might be higher than the forward price. [6 marks] (b) The current price of Stock X is $25. The stock pays no dividends. A zero-coupon default-free government bond with a face value of $100 and one year to maturity is trading at $98. You are offered a forward price for Stock X to be delivered in one year at $24.50. Comment on the validity of the following statement: "The forward price is lower than the spot price because the market anticipates a sharp decline in the price of Stock X, and the contract offers a way to hedge this risk. There is no arbitrage opportunity." (If you believe that there is an arbitrage opportunity, specify the arbitrage strategy). [6 marks] Use the following information to answer parts (c) to (f). A small engineering firm is commencing trials for a new battery technology. These trials will take one year to complete. The firm's shares are currently trading at $12 per share. The firm does not pay dividends and is not expected to do so in the next two years. If the trials are unsuccessful, the firm will be closed, and its patents sold for $5 per share. If the trials are successful, its share price will increase to $27.35 and the firm will need to apply for regulatory approval, which will require further trials that will take one year to complete. If the firm is successful in obtaining regulatory approval, the firm will be sold to a major technology company for $55 per share. If approval is not gained, the firm will be clos } ? d, and its patents sold for $15 per share. At each stage, the probability of success is the same. The firm has zero systematic risk. The risk-free rate is 3% per year and the market risk premium is 6%. (c) According to the CAPM, what should be the expected return on the firm's shares? [3 marks] (d) An investor has an agreement with the firm giving her the right, but not the obligation, to acquire the firm's shares in two years' time at the current market price of $12. What is the market value of the investor's right? [7 marks] (e) Suppose instead that the right in (d) was American. A trader offers to purchase the right from the investor at the price calculated in (d). Should the investor accept it (i.e., is the offered price fair)? Explain. [5 marks] (f) What is the value of a security that pays $1 if the firm secures regulatory approval in the next two years, and otherwise pays zero? Explain. [6 marks]